Appiah states, “…one thing that is right in the Positivist picture is this: The methods of the natural sciences have not led to the kind of progress in our understanding of values that they have led to in our grasp of facts.” Also he writes, “There is only one reality, and theories about witchcraft, like the germ theory of disease, are attempts to understand that one reality.” I think these two quotes make a good point towards the meaning of his argument.
Facts tend to be rigid. They are definite, the “one reality” that Appiah mentions, while values vary from person to person. People interpret facts based on their own values and beliefs, so although there may be “one reality” there could be many interpretations of it. Also, we usually see science as a way to pursue facts, straight answers about the way things work. We have a pretty good grasp of that so far, based on things we’ve accomplished (HIV/AIDS treatment and prevention, weather predictions, etc.) and how we’ve refined our approach to understanding the world in order to come to these conclusions more easily and accurately, but since values are so varied and individual, there is rarely a “one reality” to pursue when it comes to our grasp on them.
Because our interpretation of facts is heavily influenced by our own beliefs, it is difficult to separate the two. One person may believe in witchcraft because they were raised under the belief that it exists, and they have their own personal theories to support it, and another person might not because they were raised under the belief that it does not exist, and they, in turn, will also have their own personal theories as to why.

Related

You talked a lot about the “one reality” that Appiah was trying to present in Chapter 3. Examples of why most people believe in factual evidence is because of the current successes in finding medical issues and other problems (i.e. the prevention for the HIV/AIDS virus). What could possibly be a good explanation for witchcraft if one believes in it?

In the chapter Appiah makes it clear that regardless of the explanation of practicing witchcraft, the opposition of that is trying to explain why they are wrong. But can you explain to them exactly how western medicine works? If they’re not familiar with it, they aren’t going to trust it. Witchcraft is what they are familiar with and it works for them, regardless of the opinion of a westerner. So it’s not really a good explanation of witchcraft but it is the reason you would stop and think before trying to change their practices.